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On Pellet$ '$s Theorem for a class of lacunary polynomials


Author: A. Melman
Journal: Math. Comp. 85 (2016), 707-716
MSC (2010): Primary 12D10, 15A18, 30C15
DOI: https://doi.org/10.1090/mcom/3011
Published electronically: July 6, 2015
MathSciNet review: 3434877
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Abstract: An important tool to separate zeros of a polynomial according to their moduli without actually computing them is Pellet's theorem, which unfortunately places severe restrictions on the polynomial's coefficients. We show that for a class of lacunary polynomials much better results can be obtained by rewriting a polynomial as a matrix polynomial.


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Additional Information

A. Melman
Affiliation: Department of Applied Mathematics, School of Engineering, Santa Clara University, California 95053
Email: amelman@scu.edu

DOI: https://doi.org/10.1090/mcom/3011
Received by editor(s): April 14, 2014
Received by editor(s) in revised form: August 26, 2014
Published electronically: July 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society